Optimal Correlated Equilibria in General-Sum Extensive-Form Games: Fixed-Parameter Algorithms, Hardness, and Two-Sided Column-Generation

We study the problem of finding optimal correlated equilibria of various sorts: normal-form coarse correlated equilibrium (NFCCE), extensive-form coarse correlated equilibrium (EFCCE), and extensive-form correlated equilibrium (EFCE). This is NP-hard in the general case and has been studied in special cases, most notably triangle-free games, which include all two-player games with public chance moves. However, the general case is not well understood, and algorithms usually scale poorly. First, we introduce the correlation DAG, a representation of the space of correlated strategies whose size is dependent on the specific solution concept. It extends the team belief DAG of Zhang et al. to general-sum games. For each of the three solution concepts, its size depends exponentially only on a parameter related to the game's information structure. We also prove a fundamental complexity gap: while our size bounds for NFCCE are similar to those achieved in the case of team games by Zhang et al., this is impossible to achieve for the other two concepts under standard complexity assumptions. Second, we propose a two-sided column generation approach to compute optimal correlated strategies. Our algorithm improves upon the one-sided approach of Farina et al. by means of a new decomposition of correlated strategies which allows players to re-optimize their sequence-form strategies with respect to correlation plans which were previously added to the support. Our techniques outperform the prior state of the art for computing optimal general-sum correlated equilibria. For team games, the two-sided column generation approach vastly outperforms standard column generation approaches, making it the state of the art algorithm when the parameter is large. Along the way we also introduce two new benchmark games: a trick-taking game that emulates the endgame phase of the card game bridge, and a ride-sharing game.

Zap: Making Predictions Based on Online User Behavior

This paper introduces Zap, a generic machine learning pipeline for making predictions based on online user behavior. Zap combines well known techniques for processing sequential data with more obscure techniques such as Bloom filters, bucketing, and model calibration into an end-to-end solution. The pipeline creates website- and task-specific models without knowing anything about the structure of the website. It is designed to minimize the amount of website-specific code, which is realized by factoring all website-specific logic into example generators. New example generators can typically be written up in a few lines of code.

The Kinetics Human Action Video Dataset

We describe the DeepMind Kinetics human action video dataset. The dataset contains 400 human action classes, with at least 400 video clips for each action. Each clip lasts around 10s and is taken from a different YouTube video. The actions are human focussed and cover a broad range of classes including human-object interactions such as playing instruments, as well as human-human interactions such as shaking hands. We describe the statistics of the dataset, how it was collected, and give some baseline performance figures for neural network architectures trained and tested for human action classification on this dataset. We also carry out a preliminary analysis of whether imbalance in the dataset leads to bias in the classifiers.